A Simple model of pathogen-mediated nutrient dynamics

How do nitrogen and phosphorus availability impact infectious disease, and what are the reciprocal effects of pathogens on ecosystem nutrient dynamics? These questions are fundamental to understanding the coupling between disease dynamics and nutrient cycles, yet disease-ecosystem relationships are often overlooked. Relationships linking infectious disease with ecosystem nutrient dynamics are multidirectional and can form feedback loops, though the dynamic interdependence of these processes is little understood. We illustrate the impact of disease-ecosystem feedback loops for the dynamics of both infection outcomes and ecosystem nutrients using a simple mathematical model. The model is a nonsmooth system of ordinary differential equations combining approaches from classical ecological models (logistic and droop growth) and epidemiological models (disease transmission). Our model incorporates the effects of nutrient availability on growth rates of susceptible and infected hosts, as well as the return of nutrients to the environment following host death. Despite the simplicity of this model, our results illustrate complex dynamics in host populations, infection patterns, and ecosystem nutrients that can arise from even a simple disease-nutrient feedback.